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Dmitry_Shevchenko [17]

1 year ago

14

A website randomly selects among 10 products to discount each day. The color printer of interest to you is discounted today. Det

ermine the following:_______.
(a) What is the probability that this product is first discounted again exactly 10 days from now?
(b) What is the expected number of days until this product is again discounted?

1 answer:

Varvara68 [4.7K]1 year ago

6 0

Answer:

a) P = 0.039

b) The expected number of days is 10 days.

Step-by-step explanation:

The most appropiate distribution to use in this case is the geometric distribution, in order to calculate the probability of a success after k failure trials.

The probability of success, as each of the 10 products are assumed to have fair probabilities, is:

$p=1/10=0.1$

Then, the probability that our product is not selected any given day is:

$q=1-p=1-0.1=0.9$

a) The probability that exactly this product is selected exactly 10 days from now is the probability that is not selected (probbility q) for the next 9 days and selected (probability p) at the 10th day:

$P=q^9p^1=0.9^9\cdot0.1=0.3874\cdot0.1=0.039$

b) The expected number of days is calculated as:

$E(X)=\dfrac{1}{p}=\dfrac{1}{0.1}=10$

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